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Math Help - Kern and Bland Solid Mensuration problem 18 pg8

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    Kern and Bland Solid Mensuration problem 18 pg8



    Each of the four circles shown in the figure above is tangent to the other three.
    (a) If the radius of each of the smaller circles is a, find the area of the largest circle.
    (b) If a = 2.71 what is the area of the largest circle?



    Please help me. Thanks!
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    Quote Originally Posted by cutiemike1 View Post


    Each of the four circles shown in the figure above is tangent to the other three.
    (a) If the radius of each of the smaller circles is a, find the area of the largest circle.
    (b) If a = 2.71 what is the area of the largest circle?

    connect the centers of the three smaller circles, which forms an equilateral triangle with side length 2a.

    height of this equilateral triangle (which is also a median) is a\sqrt{3}

    the centroid of the equilateral triangle is the center of the large circle ... you need to calculate the distance along the median from the triangle's vertex to the centroid, and add that distance to a to get the large circle's radius.

    recall the ratio that a centroid divides a median.
    Thanks from mventurina1
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    Quote Originally Posted by cutiemike1 View Post


    Each of the four circles shown in the figure above is tangent to the other three.
    (a) If the radius of each of the smaller circles is a, find the area of the largest circle.
    (b) If a = 2.71 what is the area of the largest circle?



    Please help me. Thanks!
    ... as usual I'm too late with my answer. So I only post the sketch which illustrates skeeter's way of solving your question.
    Attached Thumbnails Attached Thumbnails Kern and Bland Solid Mensuration problem 18 pg8-packedcircles.png  
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    earboth ... what are you using to make such a nice diagram?
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    Quote Originally Posted by skeeter View Post
    earboth ... what are you using to make such a nice diagram?
    Guten Abend,

    have a look here: euklid dynageo homepage

    1. It's more or less the standard software in German schools to do geometric constructions.
    2. It is a dynamic program that means you are able "to pull" at points or line segments and watch how the figure is changed.
    3. You can "record" the path of a point if you change the property of a drawing (see attachment)
    4. The program costs some .
    5. I don't know if there is an English version available.

    6. You can use the program as a shareware version but (I believe) you can't save your constructions.

    If necessary contact me for further informations by pm.
    Attached Thumbnails Attached Thumbnails Kern and Bland Solid Mensuration problem 18 pg8-krse_yachsentang.png  
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    .i'm very sorry sir, i get the idea of how to do it, but i don't know how to get the centroid of a triangle and its median.
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    Quote Originally Posted by cutiemike1 View Post
    .i'm very sorry sir, i get the idea of how to do it, but i don't know how to get the centroid of a triangle and its median.
    then you have something to research on your own. try googling triangle centroid.
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    Quote Originally Posted by skeeter View Post
    then you have something to research on your own. try googling triangle centroid.
    i researched about the triangle centroid and what i can only find out is the centriod of a right triangle. now, should i multiply it by 2 because it's equilateral triangle? so it will become 2(a+b+c)/3 ?
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    The centroid of a triangle divides each one of its medians in the ratio 2:1
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